I guess nobody is responding because it is easier to do than to explain.
John meant 'recoil housing' where he said 'saw'.
Carefully remove the rope pulley from the housing. Do NOT let the spring pop out, or you will spend 30-45 minutes trying to rewind it and put it back in.
Remove the old rope, feed the new rope (same size, NOT fatter- it will bind if you use too big of a rope and your rope will be too short) through the hole in the housing and through the hole in the pulley and tie it off. I melt the end of the knot to keep it from untying later.
Replace the pulley into the housing.
Grab the string in between the pulley and where it comes through the housing and pull up some slack. Needlenose pliers help if you can't get your finger in there. While holding that part of the string against that spot on the pulley, wind the pulley counter-clockwise a few turns. Then let the spring pull the line in. If your handle is still loose, repeat another turn or two untill the handle is snug to the outside of the housing.
Replace the housing with working recoil on the saw.
I've done hundreds of these, it's much easier to do than to explain.
Anybody jump in if I missed anything.